1. A small hospital is planning for future needs in its maternity wing. The data be¬low show the number of births in each of the past eight years.
|
Year
|
Births
|
Year
|
Births
|
|
1
|
565
|
5
|
615
|
|
2
|
590
|
6
|
611
|
|
3
|
583
|
7
|
610
|
|
4
|
597
|
8
|
623
|
a. Use simple linear regression to forecast the annual number of births for each of the next three years.
b. Determine the correlation coefficient for the data and interpret its meaning.
c. Find the coefficient of determination for the data and interpret its meaning.
2. Suregrip Calculator Company (SCC) needs to estimate its sales for next year. The most recent six years of revenue data for the company's popular line of calcula¬tors are given below:
|
|
Sales Revenues
|
|
Sales Revenues
|
|
Year
|
(millions of dollars)
|
Year
|
(millions of dollars)
|
|
1
|
46.7
|
4
|
77.9
|
|
2
|
59.3
|
5
|
85.1
|
|
3
|
74.2
|
6
|
98.0
|
a. Assuming that the sales data above are representative of sales expected next year, use time series regression analysis to forecast next year's (Year 7's) sales revenues.
b. Determine the correlation coefficient for the data and interpret its meaning.
c. Find the coefficient of determination for the data and interpret its meaning.
3. IPC's plant estimates weekly demand for its many materials held in inventory. One such part, the CTR 5922, is being studied. The most recent 12 weeks of demand for the CTR 5922 are:
|
|
Demand
|
|
Demand
|
|
Demand
|
|
Demand
|
|
Week
|
(units)
|
Week
|
(units)
|
Week
|
(units)
|
Week
|
(units)
|
|
1
|
169
|
4
|
171
|
7
|
213
|
10
|
158
|
|
2
|
227
|
5
|
163
|
8
|
175
|
11
|
188
|
|
3
|
176
|
6
|
157
|
9
|
178
|
12
|
169
|
Use the moving average method of short-range forecasting with an averaging pe¬riod of three weeks to develop a forecast of the demand for the CTR 5922 com¬ponent in Week 13.
4. Finley Heaters Inc. is a mid-sized manufacturer of residential water heaters. Sales have grown during the last several years, and the company's production capacity needs to be increased. The company's management wonders if national housing starts might be a good indicator of the company's sales:
|
|
National
|
Finley Heaters'
|
|
|
Housing Starts
|
Annual Sales
|
|
Year
|
(millions)
|
(millions of dollars)
|
|
I
|
6.2
|
57
|
|
2
|
5.1
|
59
|
|
3
|
6.5
|
65
|
|
4
|
7.9
|
78
|
|
5
|
6.3
|
72
|
|
6
|
7.4
|
80
|
|
7
|
7.0
|
86
|
a. Develop a simple linear regression analysis between Finley Heaters' sales and national housing starts. Forecast Finley Heaters' sales for the next two years. The National Home Builders Association estimates that national housing starts will be 7.1 million and 8.0 million for the next two years.
b. What percentage of variation in Finley Heaters' sales is explained by national housing starts?
c. Would you recommend that Finley Heaters management use the forecast from Part a to plan facility expansion? Why or why not? What could be done to improve the forecast?
5. The number of Texas tax auditors needed by the Internal Revenue Service varies from quarter to quarter. The past 12 quarters of data are shown below:
|
Year
|
Quarter
|
Auditors
|
|
1
|
1
|
132
|
|
|
2
|
139
|
|
|
3
|
136
|
|
|
4
|
140
|
|
2
|
1
|
134
|
|
|
2
|
142
|
|
|
3
|
140
|
|
|
4
|
139
|
|
3
|
1
|
135
|
|
|
2
|
137
|
|
|
3
|
139
|
|
|
4
|
141
|
a. Use moving averages to forecast the number of auditors needed next quarter if AP = 2, AP = 4, and AP = 6.
b. Which of these forecasts exhibits the best forecast accuracy over the past six quarters of historical data based on mean absolute deviation?